A Copula-Based and Monte Carlo Sampling Approach for Structural Dynamics Model Updating with Interval Uncertainty

Abstract

As the uncertainty is widely existent in the engineering structure, it is necessary to study the finite element (FE) modeling and updating in consideration of the uncertainty. A FE model updating approach in structural dynamics with interval uncertain parameters is proposed in this work. Firstly, the mathematical relationship between the updating parameters and the output interesting qualities is created based on the copula approach and the vast samples of inputs and outputs are obtained by the Monte Carlo (MC) sampling technology according to the copula model. Secondly, the samples of updating parameters are rechosen by combining the copula model and the experiment intervals of the interesting qualities. Next, 95% confidence intervals of updating parameters are calculated by the nonparameter kernel density estimation (KDE) approach, which is regarded as the intervals of updating parameters. Lastly, the proposed approach is validated in a two degree-of-freedom mass-spring system, simple plates, and the transport mirror system. The updating results evidently demonstrate the feasibility and reliability of this approach.